Related papers: Kinetic Solvers with Adaptive Mesh in Phase Space

We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…

This paper introduces a novel approach to solving multi-block nonconvex composite optimization problems through a proximal linearized Alternating Direction Method of Multipliers (ADMM). This method incorporates an Increasing Penalization…

Adaptive Multi-Agent Systems (AMAS) transform dynamic problems into problems of local cooperation between agents. We present smapy, an ensemble based AMAS implementation for mobility prediction, whose agents are provided with machine…

We present here the first systematic treatment of the problems posed by the visualization and analysis of large-scale, parallel adaptive mesh refinement (AMR) simulations on an Eulerian grid. When compared to those obtained by constructing…

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods…

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of ECP applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion,…

This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation…

Adjoint based shape optimization is a powerful technique in fluid-dynamics optimization, capable of identifying an optimal shape within only dozens of design iterations. However, when extended to rarefied gas flows, the computational cost…

We deal with non-hydrostatic mesoscale atmospheric modeling using the fully implicit space-time discontinuous Galerkin method in combination with the anisotropic $hp$-mesh adaptation technique. The time discontinuous approximation allows…

We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are…

An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…

We describe a fast, direct solver for elliptic partial differential equations on a two-dimensional hierarchy of adaptively refined, Cartesian meshes. Our solver, inspired by the Hierarchical Poincar\'e-Steklov (HPS) method introduced by…

Variational inequalities play a pivotal role in a wide array of scientific and engineering applications. This project presents two techniques for adaptive mesh refinement (AMR) in the context of variational inequalities, with a specific…

We generalise the non-affine theory of viscoelasticity for use with large, well-sampled systems of arbitrary chemical complexity. Having in mind predictions of mechanical and vibrational properties of amorphous systems with atomistic…

The design space of dynamic multibody systems (MBSs), particularly those with flexible components, is considerably large. Consequently, having a means to efficiently explore this space and find the optimum solution within a feasible…

A stable added-mass partitioned (AMP) algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and compressible elastic-solids. The AMP scheme remains stable and second-order accurate even…

In this paper, we propose a new adaptive technique, named adaptive trajectories sampling (ATS), which is used to select training points for the numerical solution of partial differential equations (PDEs) with deep learning methods. The key…

We present the first high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step…

With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differential Equations (PDEs). Compared to traditional methods, PINNs…

Sampling-based Motion Planners (SMPs) have become increasingly popular as they provide collision-free path solutions regardless of obstacle geometry in a given environment. However, their computational complexity increases significantly…